What is the answer to ln(x+1)=2-ln(x-1) ?

The answer to ln(x+1)=2-ln(x-1) is x=sqrt(e^2+1)

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ln(x+1)=2-ln(x-1)

ln (x + 1) = 2 - ln (x - 1)

x = e^{2} + 1

Decimal Notation

x = 2.89638 \dots

Solution steps

ln (x + 1) = 2 - ln (x - 1)

Add

ln (x - 1)

to both sides

ln (x + 1) + ln (x - 1) = 2 - ln (x - 1) + ln (x - 1)

Simplify

ln (x + 1) + ln (x - 1) = 2

Apply log rules

(x + 1) (x - 1) = e^{2}

Solve

(x + 1) (x - 1) = e^{2} : x = e^{2} + 1, x = - e^{2} + 1

x = e^{2} + 1, x = - e^{2} + 1

Verify Solutions:

x = e^{2} + 1

True

, x = - e^{2} + 1

False

The solution is

x = e^{2} + 1

lo g_{2} (x + a) = b

3.5 = - lo g_{10} (x)

lo g_{x} (10) = \frac{1}{3}

2 lo g_{10} (x) = 0

2 lo g_{10} (x + 5) = lo g_{10} (x + 7)

What is the answer to ln(x+1)=2-ln(x-1) ?
The answer to ln(x+1)=2-ln(x-1) is x=sqrt(e^2+1)
Solve for x: ln(x+1)=2-ln(x-1)
The solution is x=sqrt(e^2+1)